Most of the time, special options will be available based on Speech check. The option will always be there, but the success chance is based on your Speech skill.
Once in a while, you might get another special option based on another stat or skill, only IF THAT SKILL IS HIGH ENOUGH. So, you might get an extra option for having say Science 60+ when talking to someone. Without that, the option won't appear at all.
Now, when you see those extra options come up (it tells you the stat/skill that made it available), they will ALWAYS work. It's basically a free option as long as you meet the requirements.
However, be aware that it doesn't mean they're the best thing to say for the conversation. Some of them will actually get you a negative reaction. They won't "fail", because there's no check or anything... they're just the wrong thing to say (like insulting someone).
Basically, based on your speech skill, when you have to make a speech check (the line will always be visible in conversations) it will say something like [SPEECH: 35%] <insert line here> which you have a chance of failing based on your speech check. Increasing your speech skill will increase that percentage.
The other type of stat based conversations will only be visible if you have a high enough value in that stat, so for example [INTELLIGENCE] <insert line here> which means that that line is only available because you have a high enough intelligence stat. This line will always "succeed", but it doesn't necessarily mean that you'd want to use that line whenever possible. It just gives you an additional response choice, to play the game more like you want it to.
Now, I'm fairly sure that there is a line for Charisma checks in the Survival Guide side quest. There are probably a few more out there, but if you don't want to have a high charisma, you don't have to.
[This signature was deleted at the request of a lesser deity]
No kidding, I'm practically grasping at straws trying to find a reason, any good reason to invest in Charisma... cause for the weirdest reason, I like the idea of my character being pretty and polite. Charisma is suppose to improve initial disposition, but exactly how you're suppose to measure that is beyond me.
Charisma was very useful in Fallout 2, if anything for getting a huge party of expendable bag handlers and humans shields, but In Fallout 3, I haven't seen a particularly good reason to invest in Charisma instead of just tagging Speech and Barter. Child at Heart might be worth taking with 4 points of Charisma, but I just can't see the rest of the Charisma related perks as being particularly useful unless you like the idea of animals randomly helping you in battle. I haven't taken it before, but just how useful is Child at Heart anyway?